Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps

Abstract

In this article, we present an event-driven algorithm that generalizes the recent hard-sphere event-chain Monte Carlo method without introducing discretizations in time or in space. A factorization of the Metropolis filter and the concept of infinitesimal Monte Carlo moves are used to design a rejection-free Markov-chain Monte Carlo algorithm for particle systems with arbitrary pairwise interactions. The algorithm breaks detailed balance, but satisfies maximal global balance and performs better than the classic, local Metropolis algorithm in large systems. The new algorithm generates a continuum of samples of the stationary probability density. This allows us to compute the pressure and stress tensor as a byproduct of the simulation without any additional computations.

References in corpus (8)

• Two-step melting in two dimensions: First-order liquid-hexatic transition
• Shortcomings of the Bond Orientational Order Parameters for the Analysis of Disordered Particulate Matter
• Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods
• Event-chain Monte Carlo algorithms for hard-sphere systems
• Rejection-free Geometric Cluster Algorithm for Complex Fluids
• Rejection-free Monte-Carlo sampling for general potentials
• Irreversible Monte Carlo Algorithms for Efficient Sampling
• Sampling from a polytope and hard-disk Monte Carlo

Cited by in corpus (87)

• 2D Melting: From Liquid-Hexatic Coexistence to Continuous Transitions
• Scalable Metropolis Monte Carlo for simulation of hard shapes
• Piecewise-Deterministic Markov Chain Monte Carlo
• The race to the bottom: approaching the ideal glass?
• Ergodicity of the zigzag process
• Event-chain Monte Carlo: foundations, applications, and prospects
• Hard-sphere melting and crystallization with event-chain Monte Carlo
• Disappearance of the hexatic phase in a binary mixture of hard disks
• Event-chain Monte Carlo for classical continuous spin models
• Irreversible local Markov chains with rapid convergence towards equilibrium
• Newtonian Event-Chain Monte Carlo and Collision Prediction with Polyhedral Particles
• Event-chain Monte Carlo algorithms for three- and many-particle interactions
• Event-chain algorithm for the Heisenberg model: Evidence for $z\simeq 1$ dynamic scaling
• Monte Carlo Simulation of Dense Polymer Melts Using Event Chain Algorithms
• Cell-veto Monte Carlo algorithm for long-range systems
• Phase transitions and ordering structures of a model of chiral helimagnet in three dimensions
• Eigenvalue analysis of an irreversible random walk with skew detailed balance conditions
• All-atom computations with irreversible Markov chains
• Efficient Equilibration of Hard Spheres with Newtonian Event Chains
• Sampling efficiency of transverse forces in dense liquids
• Fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of long-range interacting systems
• Efficient Irreversible Monte Carlo samplers
• Irreversible Monte Carlo algorithms for hard disk glasses: from event-chain to collective swaps
• Clustering and assembly dynamics of a one-dimensional microphase former
• Clock Monte Carlo methods
• JeLLyFysh-Version1.0 -- a Python application for all-atom event-chain Monte Carlo
• Parallelized event chain algorithm for dense hard sphere and polymer systems
• Population Annealing Simulations of a Binary Hard Sphere Mixture
• Event-Chain Monte-Carlo Simulations of Dense Soft Matter Systems
• Irreversible Markov chains in spin models: Topological excitations
• Mixing and perfect sampling in one-dimensional particle systems
• Dynamical computation of the density of states and Bayes factors using nonequilibrium importance sampling
• Event-chain Monte Carlo with factor fields
• Multithreaded event-chain Monte Carlo with local times
• Monte Carlo simulations of glass-forming liquids beyond Metropolis
• Chaining of hard disks in nematic needles: particle-based simulation of colloidal interactions in liquid crystals
• Exchanging replicas with unequal cost, infinitely and permanently
• Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk
• Hard-disk dipoles and non-reversible Markov chains
• PDMP characterisation of event-chain Monte Carlo algorithms for particle systems
• A general perspective on the Metropolis-Hastings kernel
• Concepts in Monte Carlo sampling
• Non-reversible Monte Carlo: an example of 'true' self-repelling motion
• Irreversible Boltzmann samplers in dense liquids: weak-coupling approximation and mode-coupling theory
• Molecular simulation from modern statistics: Continuous-time, continuous-space, exact
• Effect of particle size distribution on polydisperse hard disks
• Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models
• Large-scale dynamics of event-chain Monte Carlo
• Sparse hard-disk packings and local Markov chains
• Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains
• Control of probability flow in Markov chain Monte Carlo -- Nonreversibility and lifting
• Complexity of zigzag sampling algorithm for strongly log-concave distributions
• Characterising the slow dynamics of the swap Monte Carlo algorithm
• Non-reversible lifts of reversible diffusion processes and relaxation times
• Characterization and Efficient Monte Carlo Sampling of Disordered Microphases
• Direction-sweep Markov chains
• Irreversible swap algorithms for soft sphere glasses
• The Coordinate Sampler: A Non-Reversible Gibbs-like MCMC Sampler
• Sampling algorithms in statistical physics: a guide for statistics and machine learning
• Clock Factorized Quantum Monte Carlo Method for Long-range Interacting Systems
• Fast event-driven simulations for soft spheres: from dynamics to Laves phase nucleation
• The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study
• Lifted directed-worm algorithm
• Metropolis Monte Carlo sampling: convergence, localization transition and optimality
• Velocity trapping in the lifted TASEP and the true self-avoiding random walk
• Phase Boundaries of Bulk 2D Rhombi
• The virial theorem with periodic boundary conditions
• Markov-chain sampling for long-range systems without evaluating the energy
• Microscopic Mechanisms of Diffusion Dynamics: A Comparative Efficiency Study of Event-Chain Monte Carlo Variants in Dense Hard Disk Systems
• Reducing rejection exponentially improves Markov chain Monte Carlo sampling
• Comparison of the clock, stochastic cutoff, and Tomita Monte Carlo methods in simulating the dipolar triangular lattice at criticality
• Avoiding critical slowdown in models with SALR interactions
• Piecewise deterministic sampling with splitting schemes
• Computational Methods toward Ultrastable Glasses
• Event-chain Monte Carlo simulations of the liquid to solid transition of two-dimensional decagonal colloidal quasicrystals
• Bosonized one-dimensional quantum systems through enhanced event-chain Monte Carlo
• Multi-scale time-stepping in molecular dynamics
• Phase Transitions for Cuboc Orders in Stacked Kagome Heisenberg Systems
• Melting and re-entrant melting of polydisperse hard disks
• Necessary and sufficient symmetries in Event-Chain Monte Carlo with generalized flows and Application to hard dimers
• Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs
• Hypocoercivity meets lifts
• Lifted TASEP: long-time dynamics,generalizations, and continuum limit
• The generic Mott transition in the sine-Gordon model through an embedded worm algorithm
• Emergence of Nonequilibrium Latent Cycles in Unsupervised Generative Modeling
• Accelerating Multicanonical Sampling with Irreversibility
• Kinetic Event-Chain Algorithm for Active Matter